32 R. Rueeies Gates AND GEO. E. Darsy.—Blood Groups and

the capacity for producing certain new mutations may arise during the life-time of a species.
In the case of the blood groups, which are generally agreed to have arisen as dominant mutations
and which apparently began at different periods in the history of human races, we must then
‘suppose that at a particular period in early human history the A blood group began to occur
as a mutation with a frequency of say one in a million in a particular strain. Hach time such
a mutant occurred his or her descendants would transmit the condition; and so it would
‘continue to spread (being innocuous) partly by inheritance and the movements of peoples,
and partly by the recurrence of fresh mutations. Probably the white Indians of Darien have
become numerous in the same way, not because all are descended from a single recessive mutant,
but because that particular strain of Indians, for some unknown reason, bezan centuries ago
to produce repeated albino mutations with a low but relatively stable frequency. But this
form of albinism is recessive to normal in inheritance, while the A and B blood groups are
both dominant to O.

On this hypothesis we would therefore assume that a particular early strain of the human
race or of Homo sapiens began to produce the mutation which results in the blood group A,
which gradually spread by the combined effects of repeated mutations and inheritance until
such outlying people as the Australian aborigines, the Bushmen, the Lapps and the Maori
were more or less permeated with it. It has frequently been assumed that A arose in Western
Europe and spread from there ; but if it is old enough to be represented in a large percentage
of the primitive Bushmen and Australians and the isolated Hawaiians, then evidence regarding
its original centre of dispersal is probably no longer obtainable, except that it must have arisen,
like B, in the Eastern hemisphere. The B blood group will then have taken a similar origin
at a later time, in a strain in which A was already prevalent. Recognizing that the highest
known percentages of B now occur in Southern and Hastern Asia, among the Hindoos, Chinese,
and Manchurians, as well as among the West African negroes, it is reasonable to regard Central

Asia as a centre of its dispersal, with possibly an independent mutational origin and spread in
Africa.

1 J am indebted to my friend Professor R. A. Fisher, F.R.S., for the following analysis of the spread of a
character through repeated mutation, in the absence of selection.

Assume that of all normal gametes in the population, the fraction 1 mutate in each generation. Then
l—y. gametes remain normal, and after generations (1 — p.)” will remain normal.

Let (l—p)"=g. Then p= 1 —q is the proportion of mutated gametes. With random mating in
each generation the three zygotic types are therefore in the well-known ratio g? normal : 2pg heterozygotes :
p* homozygous mutants. Since yu is certainly small, g will only differ appreciably from unity when 7 is large.
In this case the expression (1 — wu)" may be replaced by e-"#, so that

g =e"
or nu = loge g

Applying this formula, if we assume that the mutation frequency is 1 in a million, then with 10,000
generations 4 = 10-*, n = 104 and p will be approximately 1 per cent. Or if u = 10-5 and m = 10! (say in
a period of 250,000 years) then p = 10 per cent. This indicates possibly too slow a rate of spread of the
blood groups in relation to the age of the human race and the probable mutation rate. Selection would, of

course, hasten the spread, but there is no reason to assume that it plays any part in connection with the
blood groups.